Mathematical problems of computerized tomography
Mathematical problems of computerized tomography
复制标题
计算机断层扫描的数学问题
DOI：
10.1109/proc.1983.12596
复制
发表时间：
1983
影响因子：
20.6
通讯作者：
F. Natterer
中科院分区：
文献类型：
--
作者：
A. Louis;F. Natterer
在计算机断层扫描中测量的数据;例如，必须处理X射线断层摄影中的X射线衰减或核磁共振断层摄影中的共振现象，以产生医生的诊断评估所基于的图像。这个过程包括解决以下数学问题。数据依赖于所搜索的分布，并且这种依赖性可以被描述为积分变换。为了产生最后的图像，相当于积分变换的逆变换。本文讨论了计算机层析成像中不同技术的积分变换模型。除其他事项外，还讨论了以下问题。在反演变换时，我们必须遇到哪些数值问题;例如，依赖于数据的准确性，我们可以期望重建的准确性。一个分布在多大程度上是由有限数量的测量所决定的。如果数据不完整，是否有可能可靠地恢复分布。
The data measured in computerized tomography; e.g., the X-ray attenuation in X-ray tomography or the resonance phenomena in nuclear magnetic resonance tomography, have to be processed to produce the pictures on which the diagnostic evaluation of the physician is based. This process consists of the solution of the following mathematical problem. The data depend on the searched-for distribution and this dependence can be described as an integral transform. To produce the final picture amounts to the inversion of the integral transform. This paper is concerned with the description of the integral transforms modeling the different techniques in computerized tomography. Among other things, the following questions are treated. Which numerical problems do we have to encounter in inverting the transforms; e.g., what accuracy in the reconstruction can we expect in dependence on the accuracy of the data. To what extent is a distribution determined by a finite number of measurements. Is it possible to recover the distribution reliably if the data are incomplete.